Stefan-Boltzmann Power Calculator
The Stefan-Boltzmann law gives the thermal radiation power emitted by a surface as a function of its absolute temperature. It underpins calculations for radiative cooling, infrared thermography, incandescent lighting, spacecraft thermal control, and stellar luminosity. Because the radiated power rises with the fourth power of temperature, even a small temperature change has a large effect. Enter the emissivity, surface area, surface temperature in kelvin, and a surrounding temperature; this calculator returns the gross radiated power, the radiant exitance per square metre, and the net power exchanged with the surroundings.
Stefan-Boltzmann formula
sigma = 5.670374419e-8 W/m^2/K^4
Radiant exitance = e * sigma * T^4
Radiated power = e * sigma * A * T^4
Net power = e * sigma * A * (T^4 - T_surr^4)
Black-body exitance = sigma * T^4
T and T_surr are absolute temperatures in kelvin. Emissivity e is dimensionless and equals 1 for an ideal black body. Net power is positive when the surface is hotter than its surroundings, meaning it loses heat by radiation.
Radiative heat transfer context
- The Stefan-Boltzmann constant is exactly derived from the Boltzmann constant, Planck constant, and speed of light fixed in the 2019 SI redefinition.
- Because power scales with T^4, doubling absolute temperature increases radiated power sixteenfold.
- Polished aluminium has emissivity near 0.05, while matte black surfaces and most painted, oxidised, or organic surfaces exceed 0.9.
- The net radiation term matters whenever surroundings are not far below the object temperature, such as room-temperature heat exchangers.
- Convert Celsius to kelvin by adding 273.15 before entering the temperature.
Stefan-Boltzmann law: frequently asked questions
What is the Stefan-Boltzmann law?
The Stefan-Boltzmann law states that the total power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature. For a real surface the radiated power P equals emissivity times the Stefan-Boltzmann constant times area times temperature to the fourth power: P = e x sigma x A x T^4.
What is the value of the Stefan-Boltzmann constant?
The Stefan-Boltzmann constant sigma equals 5.670374419 x 10^-8 watts per square metre per kelvin to the fourth power (W/m^2/K^4). It is an exactly derived constant in the SI system, fixed by the defined values of the Boltzmann constant, Planck constant, and speed of light.
What is emissivity?
Emissivity is a dimensionless number between 0 and 1 describing how effectively a surface radiates thermal energy compared to an ideal black body. A perfect black body has emissivity 1. Polished metals can be below 0.1, while matte black paint, soot, and most natural surfaces are above 0.9.
Do I have to use kelvin for temperature?
Yes. The Stefan-Boltzmann law uses absolute temperature, so you must convert from Celsius by adding 273.15, or from Fahrenheit by first converting to Celsius. Using degrees Celsius or Fahrenheit directly produces a meaningless result because the law depends on the fourth power of the absolute scale.
What is net radiated power for an object in surroundings?
An object both emits and absorbs thermal radiation. The net power radiated to surroundings at temperature T_surr is P_net = e x sigma x A x (T^4 - T_surr^4). This calculator reports both gross emitted power at the object temperature and net power against your chosen surrounding temperature.
Official sources
- NIST Fundamental Physical Constants: CODATA Stefan-Boltzmann constant.
- NIST Physical Measurement Laboratory: SI units and quantities (SP 811).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.